Did some crossbow mathematics today

[XB I GO]

Since there was no school today I took out the chronograph and did some experimenting. First I weighed different bolts and had 10 weights. Then I shot each bolt 3 times over the chronograph from the Axiom and 3 times from the M380. I averaged the 3 shot velocity. Then I figured out the weight to velocity and came up with this: Every increase of 1.0 grains of arrow weight = 1.27 feet per second loss in velocity. It was a long boring day.

[robertyb]

I am wondering if you messed up somewhere in your calculations. The accepted norm is for every 3 grains of added weight you loose 1 fps in speed. Thus going from 350 grains to 400 grains you would loose approximately 17 fps. By your calculation you would loose approx. 63.5 fps.

Of course I am assuming that by velocity in a crossbow you mean speed.

[janesy]

On all of my Micro's and matrix's I've ran over a chrony, a Flemish string and 50grns accounted for a 7% loss
5% for the 50grns(350 to 400 increase)
2% for the string

The percentage fluctuated slightly depending on the string, the biggest variance being .7%(6.3%loss)less loss with an abnormally fast string. But for the sake of an estimate from a stock setup 7% has proven to be very consistent.

[XB I GO]

I'm not great at math!

376.4 grain bolt weight average with 288 fps average 0/0

390.6 grain bolt weight average with 271 fps average. 14.2 grain increase = 17 fps decrease

402.5 grain bolt weight average with 258 fps average. 11.9 grain increase = 13 fps decrease

I reduced the # of arrows I used so I changed the average a little.

Can someone work that out properly?

Do I divide the weight by speed or speed by weight? One way this shows .87 grains = 1 fps or the other way it shows -1.14 fps = 1 grain. I do not get 3 grains or fps anything the way I am doing it. From the lightest bolt to heaviest is 26 grains and I am losing 30 fps and there's my 1.14....

This is what I got reducing it to 3 shot averages and then averaging the velocity from the two crossbows. Weighed every arrow and the 376.4's are all exact, the other varied 1 or 2 grains but no more than that and I averaged the weight.

Thanks

[nchunterkw]

One way this shows .87 grains = 1 fps or the other way it shows -1.14 fps = 1 grain.

This is the same thing. 0.87 gr/fps = 1.14fps/gr. Look at the units. They are 1 over each other. 1/.87 = 1.14. It's just how you are stating it.


When using averages, you start to muddle things to some degree. Check you data and calculate the fps/gr for each individual measurement. Does anything stand out as "too high" or "too low". These would be what we call "out of family" measurements. For example: If you measure your bow and get

301.25 fps
302.55 fps
300.35 fps
301.05 fps
306.5 fps
302.25 fps

something is off with that 306 right? It's too different from the others. So you would eliminate that measurement.

Separate them out as well by bow. Different bows apply the energy to the rows differently. The typical rule of thumb we use on this forum(verified by many different folks) is typically 1 fps/5 gr for an older EXO series bow, and somewhere around 1fps/2 - 3gr for the Matrix and Micros.

When doing this kind of stuff it is very important to do everything EXACTLY the same as best you can. Same distance from the chrony, same height above the chrony eye, try to keep anything and everything you can think of the same between measurements so the only difference is the arrow. I actually mark the poles on my chrony with a Sharpie so I shoot over it at the same height. There is a sweet spot distance above the eyes that you want to be. The chrony will tell you in the literature. I then put my bow on sand bags and use a laser bore sighter to make sure the arrow is launching through the center of that window. The more attention you pay to the small details, the better your data will be. Then you can draw meaningful conclusions from that data. If the data is a mess, then the conclusions will be a mess too.

I think this is a great exercise for you to do , and will teach you a lot of real world type things that can apply across all kinds of situations.

[SEW]

There are at least two additional factors that prevent having an exact ‘/sec loss per grain loss: draw length and actual speed . Longer draw length and slower crossbow will loose less (percentage-wise) as arrow weight goes up. So, in actuality, you can only truly be accurate for a given crossbow. A 17” power stroke will loose a lot less speed per grain addition than a 9” power stroke. At least, this has been my experience with much lesser power stroke differences.
Please feel free to differ. We’re all on here to learn and share or should be.

[ThunderXB]

I was told there would be NO math!

[janesy]

There are at least two additional factors that prevent having an exact ‘/sec loss per grain loss: draw length and actual speed . Longer draw length and slower crossbow will loose less (percentage-wise) as arrow weight goes up. So, in actuality, you can only truly be accurate for a given crossbow. A 17” power stroke will loose a lot less speed per grain addition than a 9” power stroke. At least, this has been my experience with much lesser power stroke differences.
Please feel free to differ. We’re all on here to learn and share or should be.

I agree, this was my findings as well. The 308 lost less than the 370. Although, the numbers were minimal.
The 308 was around 6.75% and the 370 up to 7.5%. With all other combinations landing in between.

[SEW]

I was told there would be NO math!

I did, but it was hard to do. My college minor is in math.

[ThunderXB]

Steve, That explains a lot, MY double major was in History and English

[XB I GO]

My Dad has a Masters in English and Literature. He tells me in math any grade more than a 70 is overkill. Lol...

[janesy]

My Dad has a Masters in English and Literature. He tells me in math any grade more than a 70 is overkill. Lol...

Remember, the guy who built your Dad's house probably was better at math than literature. It takes all kinds. Math is one of those things that comes back later in life and makes much more sense